**6. Verification of the waveguide-resonance mechanism**

The direct verification of the waveguide-resonance mechanism manifestation for the X-ray beam propagation can be found in the work of Japanese scientists [45]. The work was devoted to the transport property study of the angular structure as shown in **Figure 12a**. Japanese authors measured the MoKα flux intensity dependence on magnitude of the taper angle between two Si planar reflectors forming the radiation transportation structure. **Figure 12b** demonstrates the results of the measurements. The diffuse extremum *I* (near 0.1°) corresponds to reaching the critical total reflection angle for the molybdenum radiation on the silicon surface. The second extremum appearing near 0.007° cannot be explained without using the waveguide-resonance concept. The growth of X-ray radiation transport efficiency connected with this maximum reflects the transformation effect from the multiple total reflection propagations to the mechanism of the waveguide-resonance flux stream. The increase of an emergent beam intensity connects with a decrease in the flux attenuation featured for the waveguide-resonance propagation mechanism. The intensity of the second extremum is half of the first one, and the width of it is smaller than the first one on approximately one order. In result, the beam corresponding to the second radiation maximum will be characterized by the enhanced radiation density. The discussed results can be conceded as the independent confirmation of the waveguide-resonance mechanism objective reality for the quasimonochromatic X-ray flux propagation through the extended nanosize slit clearances.

#### **Figure 12.**

*Experimental scheme for the study of the radiation flux transporting peculiarities featured for the angular structure built on the basis of two Si reflectors under the variation of the taper angle between them (a), and the experimental diagram reflecting the emergent beam intensity dependence on the taper angle magnitude (b) [45].*

### **7. Specific properties of PXWR**

The waveguide-resonance mechanism is characterized by some specific properties of the quasimonochromatic radiation flux propagation through narrow extended slits, and the coherence length parameter is the limiting factor for the mechanism realization. The white radiation generated by X-ray tube is not characterized by parameter of the coherence length owing to the nature of this radiation arising [46]. But the experimental data presented in **Figure 13** show that the white radiation is transported by PXWR. At the same time, its related deposit at the total intensity of X-ray beam formed by PXWR is smaller than one in the beam formed by slit-cut system. So, one can expect that the spatial coherence degree for the white

#### *Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize… DOI: http://dx.doi.org/10.5772/intechopen.93174*

radiation generated by X-ray tube is smaller than this parameter featured for X-ray quasimonochromatic lines. **Figure 13** shows that the white component intensity falls down approximately two times in all spectral ranges investigated in the experiments. Thus, a planar X-ray waveguide resonator cannot be considered as a restrictive filter for the hard white radiation. But PXWR application for X-ray beam formation decreases the white radiation deposit in the total beam intensity. This effect will be greatest for the smallest slit clearance width. The specific feature of PXWR is the impossibility to use it for β-filtration of X-ray tube initial radiation. The β-filtration procedure for X-ray diffractometry is well known [47]. This procedure is based on the use of the thin film absorber manufactured from the material, which is characterized by the energy absorption edge intervened between *EK*<sup>α</sup> and *EK*<sup>β</sup> of the tube characteristic radiation. Similar β-filter can be built on the basis of planar monocapillar prepared by using the dielectric reflectors containing a significant concentration of atoms characterized by a suitable value of the energy absorption edge. Our direct experiments showed that the similar approach is not right for PXWR. β-Radiation flux excites the uniform interference field of X-ray standing wave in all space of PXWR air slit clearance, and the intensity attenuation is not observed.

Specific properties of PXWR are not exhausted by the peculiarities discussed above. For example, the beam formed by the waveguide resonator has the nanosize width and the enhanced radiation density. The beam is not accompanied by diffraction satellites and can be modulated by an external influence. But the planar X-ray waveguide resonator is characterized by two serious lacks. The angular divergence of the beam formed by PXWR of the simplest design is usually near 0.1°, and its real integral intensity is smaller than the integral intensities of beams formed by the slit-cut systems and the polycapillary optic devices on 1–2 orders [39]. The angular divergence of PXWR emergent beam can be decreased without influence on its integral intensity by application of PXWR with specific design, which has name as the composite planar X-ray waveguide resonator (CPXWR) [48].

**Figure 14** presents the results of comparative investigations of X-ray characteristic beam formation by PXWR with the simplest construction (a) and CPXWR (b). Left part of the figure presents the measurement schemes. Spatial distributions of X-ray intensities in beams formed by these devices are shown in the right part of the figure. Radiation capture angle is the same and is equal to Δφ<sup>1</sup> = 0.11°. Composite

#### **Figure 13.**

**6. Verification of the waveguide-resonance mechanism**

*Electromagnetic Propagation and Waveguides in Photonics and Microwave Engineering*

The direct verification of the waveguide-resonance mechanism manifestation for the X-ray beam propagation can be found in the work of Japanese scientists [45]. The work was devoted to the transport property study of the angular structure as shown in **Figure 12a**. Japanese authors measured the MoKα flux intensity dependence on magnitude of the taper angle between two Si planar reflectors forming the radiation transportation structure. **Figure 12b** demonstrates the results of the measurements. The diffuse extremum *I* (near 0.1°) corresponds to reaching the critical total reflection angle for the molybdenum radiation on the silicon surface. The second extremum appearing near 0.007° cannot be explained without using the waveguide-resonance concept. The growth of X-ray radiation transport efficiency connected with this maximum reflects the transformation effect from the multiple total reflection propagations to the mechanism of the waveguide-resonance flux stream. The increase of an emergent beam intensity connects with a decrease in the flux attenuation featured for the waveguide-resonance propagation mechanism. The intensity of the second extremum is half of the first one, and the width of it is

smaller than the first one on approximately one order. In result, the beam corresponding to the second radiation maximum will be characterized by the enhanced radiation density. The discussed results can be conceded as the independent confirmation of the waveguide-resonance mechanism objective reality for the quasimonochromatic X-ray flux propagation through the extended nanosize slit

The waveguide-resonance mechanism is characterized by some specific proper-

ties of the quasimonochromatic radiation flux propagation through narrow extended slits, and the coherence length parameter is the limiting factor for the mechanism realization. The white radiation generated by X-ray tube is not characterized by parameter of the coherence length owing to the nature of this radiation arising [46]. But the experimental data presented in **Figure 13** show that the white radiation is transported by PXWR. At the same time, its related deposit at the total intensity of X-ray beam formed by PXWR is smaller than one in the beam formed by slit-cut system. So, one can expect that the spatial coherence degree for the white

*Experimental scheme for the study of the radiation flux transporting peculiarities featured for the angular structure built on the basis of two Si reflectors under the variation of the taper angle between them (a), and the experimental diagram reflecting the emergent beam intensity dependence on the taper angle magnitude (b) [45].*

clearances.

**Figure 12.**

**158**

**7. Specific properties of PXWR**

*Experimental diffraction patterns for SiO2 (101) monocrystal specimen collected in conditions of a standard Bragg-Brentano geometry (a) and a waveguide-resonator application for the initial beam formation (b). The pattern normalization was carried out on the basis of equivalence of characteristic line intensities. Pattern (a) was registered at BSW-24 (Fe) X-ray tube regime* U *= 25 keV,* I *= 3 mA and pattern (b)* U *= 25 keV,* I *= 9 mA. Geometrical sizes at the measurements were (a)* l*<sup>0</sup> = 235 mm,* l*<sup>1</sup> = 50 mm,* l*<sup>2</sup> = 235 mm,* S*<sup>1</sup> =* S*<sup>2</sup> = 0.1 mm and (b)* l*<sup>0</sup> = 235 mm,* l*<sup>1</sup> = 50 mm,* l*<sup>2</sup> = 155 mm,* l*<sup>3</sup> = 85 mm,* S*<sup>1</sup> = 0.1 mm,* s*PXWR = 0.1 μm. The collection was carried out without a pulse discrimination.*

**Figure 14.**

*Experimental schemes and flux intensity spatial distributions for CuKαβ beams formed by PXWR (a) and CPXWR (b) [48].* S*PXWR =* S*CPXWR = 88 nm,* L*PXWR =* L*CPXWR = 100 mm,* l*<sup>1</sup> = 75 mm,* l*<sup>2</sup> = 60 mm,* l*<sup>3</sup> = 400 mm,* S*<sup>1</sup> = 0.1 mm,* L*<sup>1</sup> =* L*<sup>2</sup> = 50 mm, Δ*L *= 0.1 mm. Source regimes of BSW-24 (Cu) for both measurements* U *= 20 keV,* I *= 10 mA,* A *– filter attenuation factor* K *= 200.*

waveguide resonator differs from PXWR with the simplest construction by gap existence Δ*L* 0.1 mm between two PXWRs with the simplest construction built on the basis of short reflectors. The divergence of the waveguide emergent beams was studied by the method of the step-by-step detector scanning. The angular size of the detector slit S1 was near 0.01°. The scanning step was Δ(2θ) = 0.02°.

show a fivefold increase in the radiation gathering power of the waveguide resonator due to the application of the input skewed radiation concentrator. Experimental value of the radiation gathering power enhancement obtained in our measurements was somewhat less than the rating. It is presumably explained by the nonoptimal length and form of the tapers. Nevertheless, the above result allows to state that the application of the input skewed concentrator is a powerful tool for the radiation gathering power enhancement of the waveguide-resonance structures, which provides the system modification without a significant loss in other parameters of the

*\* is the measurement magnitude, and* I

*Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize…*

*\*\* is the intensity corrected by taking*

*Experimental schemes for the study of the intensity spatial distributions in X-ray beams formed by the waveguide resonator of a conventional construction (a) and PXWR with specific design (b) and real intensity*

In principle, there are other methods for the improvement of waveguideresonator parameters. The most drastic method of PXWR parameter modification is the building of the multi-slit waveguide-resonance structures. According to our opinion, this way is very perspective, but it entails serious problems connected with

Experiments showed that the phenomenon of X-ray flux waveguide resonance increases the efficiency of X-ray fluorescence material analysis in conditions of exciting beam total reflection on studied surface (TXRF) [50]. This method modification by PXWR including the setup of TXRF spectrometer allowed to decrease the pollution detection limits in comparison with the convention of 1–2 orders. PXWR uses in experimental scheme of the particle induced X-ray emission (PIXE) allowed to elaborate the new experimental method for surface material element diagnostic [51]. Moreover, in some specific geometries, the method can provide

The waveguide-resonance propagation of X-ray characteristic radiation fluxes can be achieved not only in frame of the external total reflection phenomenon but also at the use of the Bragg reflection. By using the Bragg-Laue waveguideresonance cell (BLWRC), it is possible to build the pulsed X-ray laser on table, which will be useful for the study of kinetic processes [52]. Based on the use of

the interference effect between the individual beams [49].

**8. Practical application of the phenomenon**

element surface analysis being free from matrix effects.

emergent beam.

**161**

**Figure 15.**

*distributions in its emergent beams.* I

*DOI: http://dx.doi.org/10.5772/intechopen.93174*

*into account the attenuator (*A*).*

Experimental intensity distributions for the beams formed by the conventional and the composite PXWRs demonstrate the Gauss form of distributions. FWHM of the peak distinguished for PXWR is Δφ<sup>2</sup> = 0.11°. At the same time, the magnitude of this parameter for CPXWR emergent beam is Δφ<sup>2</sup> = 0.05° only. Total intensities of the peaks are approximately the same. Data presented show that the gap existence leads to the beam angular constriction without intensity losses. Such result is very alike on existence of the tunneling effect in the gap space. The increasing of Δ*L* distance up to 10 mm has led to an abrupt decrease of the peak total intensity and its FWHM.

Using the modified reflectors for the waveguide-resonator building allows to solve the second PXWR problem – low integral intensity of its emergent beam. Standard quartz glass plates modified by 30 mm polished tapers with an angle of ψ = 0.5° were used for building the specific waveguide resonator (**Figure 15b**). For further radiation gathering power enhancement, the tapers were coated by HfO2 thin film. Then, Ti strips with 90 nm thickness were deposited onto one plate edges, and the waveguide-resonance structure with a slit channel width of 90 nm and a height of 4 mm was assembled. In result, we received the skewed input concentrator with an angular aperture near 1°. Next, the comparative measurements of the conventional PXWR and the modified waveguide resonator were executed. The geometric parameters of the measuring schemes are given in **Figure 15**. Intensity spatial distributions for beams formed by the tested devices are shown in the same figure. In addition, the values of the total intensity (with and without the use of attenuator *A*) and the angular divergence of the beams are also quoted therein. The distributions were obtained at radiation source operation conditions [BSW-24 (Fe), *U* = 20 keV, *I* = 10 mA].

The data show that the envelope shape and FWHM of the intensity spatial distribution for a quasimonochromatic component of the beams formed by the conventional and the modified PXWR are nearly the same. On the other hand, the total intensity of the beam formed by the modified waveguide resonator is substantially higher than the beam intensity formed by the conventional PXWR. The data

*Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize… DOI: http://dx.doi.org/10.5772/intechopen.93174*

#### **Figure 15.**

waveguide resonator differs from PXWR with the simplest construction by gap existence Δ*L* 0.1 mm between two PXWRs with the simplest construction built on the basis of short reflectors. The divergence of the waveguide emergent beams was studied by the method of the step-by-step detector scanning. The angular size

*Experimental schemes and flux intensity spatial distributions for CuKαβ beams formed by PXWR (a) and CPXWR (b) [48].* S*PXWR =* S*CPXWR = 88 nm,* L*PXWR =* L*CPXWR = 100 mm,* l*<sup>1</sup> = 75 mm,* l*<sup>2</sup> = 60 mm,* l*<sup>3</sup> = 400 mm,* S*<sup>1</sup> = 0.1 mm,* L*<sup>1</sup> =* L*<sup>2</sup> = 50 mm, Δ*L *= 0.1 mm. Source regimes of BSW-24 (Cu) for both*

*Electromagnetic Propagation and Waveguides in Photonics and Microwave Engineering*

Experimental intensity distributions for the beams formed by the conventional and the composite PXWRs demonstrate the Gauss form of distributions. FWHM of the peak distinguished for PXWR is Δφ<sup>2</sup> = 0.11°. At the same time, the magnitude of this parameter for CPXWR emergent beam is Δφ<sup>2</sup> = 0.05° only. Total intensities of the peaks are approximately the same. Data presented show that the gap existence leads to the beam angular constriction without intensity losses. Such result is very alike on existence of the tunneling effect in the gap space. The increasing of Δ*L* distance up to 10 mm has led to an abrupt decrease of the peak total intensity and its

Using the modified reflectors for the waveguide-resonator building allows to solve the second PXWR problem – low integral intensity of its emergent beam. Standard quartz glass plates modified by 30 mm polished tapers with an angle of ψ = 0.5° were used for building the specific waveguide resonator (**Figure 15b**). For further radiation gathering power enhancement, the tapers were coated by HfO2 thin film. Then, Ti strips with 90 nm thickness were deposited onto one plate edges, and the waveguide-resonance structure with a slit channel width of 90 nm and a height of 4 mm was assembled. In result, we received the skewed input concentrator with an angular aperture near 1°. Next, the comparative measurements of the conventional PXWR and the modified waveguide resonator were executed. The geometric parameters of the measuring schemes are given in **Figure 15**. Intensity spatial distributions for beams formed by the tested devices are shown in the same figure. In addition, the values of the total intensity (with and without the use of attenuator *A*) and the angular divergence of the beams are also quoted therein. The distributions were obtained at radiation source operation conditions [BSW-24 (Fe),

The data show that the envelope shape and FWHM of the intensity spatial distribution for a quasimonochromatic component of the beams formed by the conventional and the modified PXWR are nearly the same. On the other hand, the total intensity of the beam formed by the modified waveguide resonator is substantially higher than the beam intensity formed by the conventional PXWR. The data

of the detector slit S1 was near 0.01°. The scanning step was Δ(2θ) = 0.02°.

*measurements* U *= 20 keV,* I *= 10 mA,* A *– filter attenuation factor* K *= 200.*

FWHM.

**Figure 14.**

*U* = 20 keV, *I* = 10 mA].

**160**

*Experimental schemes for the study of the intensity spatial distributions in X-ray beams formed by the waveguide resonator of a conventional construction (a) and PXWR with specific design (b) and real intensity distributions in its emergent beams.* I *\* is the measurement magnitude, and* I *\*\* is the intensity corrected by taking into account the attenuator (*A*).*

show a fivefold increase in the radiation gathering power of the waveguide resonator due to the application of the input skewed radiation concentrator. Experimental value of the radiation gathering power enhancement obtained in our measurements was somewhat less than the rating. It is presumably explained by the nonoptimal length and form of the tapers. Nevertheless, the above result allows to state that the application of the input skewed concentrator is a powerful tool for the radiation gathering power enhancement of the waveguide-resonance structures, which provides the system modification without a significant loss in other parameters of the emergent beam.

In principle, there are other methods for the improvement of waveguideresonator parameters. The most drastic method of PXWR parameter modification is the building of the multi-slit waveguide-resonance structures. According to our opinion, this way is very perspective, but it entails serious problems connected with the interference effect between the individual beams [49].

#### **8. Practical application of the phenomenon**

Experiments showed that the phenomenon of X-ray flux waveguide resonance increases the efficiency of X-ray fluorescence material analysis in conditions of exciting beam total reflection on studied surface (TXRF) [50]. This method modification by PXWR including the setup of TXRF spectrometer allowed to decrease the pollution detection limits in comparison with the convention of 1–2 orders. PXWR uses in experimental scheme of the particle induced X-ray emission (PIXE) allowed to elaborate the new experimental method for surface material element diagnostic [51]. Moreover, in some specific geometries, the method can provide element surface analysis being free from matrix effects.

The waveguide-resonance propagation of X-ray characteristic radiation fluxes can be achieved not only in frame of the external total reflection phenomenon but also at the use of the Bragg reflection. By using the Bragg-Laue waveguideresonance cell (BLWRC), it is possible to build the pulsed X-ray laser on table, which will be useful for the study of kinetic processes [52]. Based on the use of

phenomenon consequences, it is possible to realize the reactions of cold nuclear fusion [53]. But the more important result of waveguide-resonance radiation propagation phenomenon discovery, we regard the possibility appearing to elaborate the function correct model for optical fibers and waveguides of light beams. Conventional model of its function is based on the light flux notion as the infinite plane wave and on the light flux transportation mechanism by planar symmetrical waveguide as the multiple internal total reflections in frame of the geometrical paradigm [54–63]. Similar approach is not right, in principle. It is well known that any radiation source generates quasimonochromatic beams with λ<sup>0</sup> mean wavelength and Δλ monochromatization degree. So, any quasimonochromatic beam is characterized by the coherence length parameter. Up-to-date optical lasers generate the beams with several tens of meters of coherence length. Owing to the core size of planar symmetrical optical waveguides varies from some micrometers to some millimeters, we can conclude that all optical waveguides and fibers are functioned in frame of the waveguide-resonance phenomenon manifestation, and instead of mode structure, it is a need to discuss the properties of uniform interference field of optical radiation standing wave.
